Solve for X: Rectangle with Perimeter 20 and Sides 4X+3 and 2X+1

Question

Look at the following rectangle:

The perimeter of the rectangle is 20.

Calculate the value of X.

00:04 First, let's find the value of X.

00:09 Remember, in a rectangle, opposite sides are the same length.

00:35 The perimeter is the total distance around the rectangle.

00:43 Now, plug in the numbers you have and solve for X.

01:15 Combine all terms that are alike.

01:30 Next, we want to get X all by itself.

01:43 And there you have it, that's the solution!

Since in a rectangle every pair of opposite sides are equal, we can claim that:

$AD=BC=2x+1$

$AB=CD=4x+3$

Since the perimeter of the rectangle is equal to 20, we can substitute the data into the formula:

$20=2x+1+4x+3+2x+1+4x+3$

$20=12x+8$

$20-8=12x$

$12=12x$

Let's divide both sides by 12:

$1=x$

$1$